🧮 algebra

1. The problem states there is a linear relationship between the number of people in tens of millions living in urban areas in the US and the number of years since 1960. 2. We are

1. Stating the problem: Simplify the expression $\left(\frac{3-7}{5}+\frac{3}{10}\right)-\left(\frac{7}{12}-\frac{1}{3}\right)$.\n\n2. Simplify inside the first parentheses:\nCalcu

1. The problem gives the equation $$y = -9x + 1830$$ where $x$ is the number of years since 1950 and $y$ is the average number of working hours per worker. 2. The Y-intercept is th

1. **State the problem:** We are given a linear relationship between the number of years since 2009, $X$, and the price per box of oranges, $Y$. We need to find the slope and the Y

1. Stating the problem: Simplify the expression $\left(\frac{7}{3}+\frac{9}{4}\right)-\left(\frac{1}{2}+1\right)$.\n\n2. Find a common denominator for the fractions inside the firs

1. Factoriser A = (x + 4)(6x - 1) + (x + 4)(7x - 2) On remarque que (x + 4) est un facteur commun.

1. Factoriser chaque expression donnée. 2. Pour A = (x + 4)(6x - 1) + (1 + x)(4 + 4)(7x - 2) :

1. The problem is to simplify the expression $ (1 + i)(2 + 3i)(4 - 3i) $ where $i$ is the imaginary unit with $i^2 = -1$. 2. First, multiply the first two complex numbers:

1. **State the problem:** Ellie and Colette are typing research papers. Ellie types 1 page per hour and already has 15 pages done. Colette types 3 pages per hour and has 3 pages do

1. **تمرين 1** 1.1. فكك العددين $x=154$ و $y=140$ إلى جداء عوامل أولية:

1. ננתח את הנתונים: הסדרה היא חשבונית עם האיבר הראשון $a_1=52$ והפרש $d=56-52=4$. 2. סכום $n$ האיברים הראשונים בסדרה חשבונית הוא לפי הנוסחה:

1. The problem is to analyze the linear function $M=4x-20$. 2. This function is in slope-intercept form $M=mx+b$ where $m=4$ is the slope and $b=-20$ is the y-intercept.

1. The problem involves points A, B, D, and E with given coordinates and values such as AB = 9.6 and AB = 1.6, and some numeric values like 3884, 705.739425, 816.37422, 35.9871, 60

1. **فكك العدد x=154 إلى جداء عوامل أولية:** - 154 عدد زوجي، إذن يقبل القسمة على 2: $$154 \div 2 = 77$$

1. We are asked to simplify the expression: $$gx^2 - 3hx^2 - 6fy^2 - gy^2 + 6fx^2 + 3hy^2$$. 2. Group like terms by variables and coefficients:

1. **State the problem:** Simplify the expression $$\frac{\left(10^{3} \cdot 20^{2}\right)^{3}}{5^{5} \cdot 2} \cdot \frac{250^{4} \cdot 8^{3}}{75^{2}}$$

1. **State the problem:** Savio drives 50 miles to work, thinking his average speed is 40 miles per hour. We need to find the arrival time if this speed is correct. 2. **Use the fo

1. **State the problem:** Simplify the expression $$\frac{14x^8}{\sqrt{7x^5}}$$. 2. **Rewrite the square root in the denominator:** Recall that $$\sqrt{a} = a^{\frac{1}{2}}$$, so

1. **Problème 20 : Consommation d'essence et distance parcourue** Une voiture consomme 7 L pour 100 km. Le prix de l'essence est 129 ¢/L, soit 1,29 par litre. Avec 10 d'essence, co

1. **State the problem:** We need to order the given expressions from least to greatest. 2. **Evaluate each expression:**

1. The problem is to draw the graph of the function $f(x) = \lfloor 2x \rfloor$ where $\lfloor \cdot \rfloor$ denotes the floor function, which maps a real number to the greatest i